The simplest black hole solution in asymptotic AdS spacetime, the eternal 3-dimensional BTZ black hole, is studied from the viewpoint of AdS/CFT duality. We identify a class of non-local correlators on the CFT side that allow us to generalize the notion of quantum gravity "S-matrix" to scattering inside the horizon. Since the interior of the horizon is a cosmological spacetime with a big bang/crunch-like singularity, our construction can be interpreted as identifying generally coordinate invariant observables of quantum gravity in a simple cosmology, and their non-perturbative realization within CFT. We show in a certain precise sense, that these holographic observables lie "before the big bang" in a region of spacetime containing closed timelike curves. A central tool in our analysis is the realization of BTZ as a quotient of 3-dimensional AdS.